EPSRC-SFI: "CFT and Gravity: Heavy States and Black Holes"

量子场论（QFT）是理论物理学中描述量子系统的通用语言，从数学物理学到现象学都有广泛的应用。当理论中量子之间的相互作用较弱时，可以使用标准技术来获得定量预测。然而，许多重要的物理现象（例如在相对高温下的超导性，强耦合等离子体的行为等）严重依赖于强相互作用，因此传统的方法失败了。在这个项目中，我们将开发必要的数学机制来描述具有强相互作用的量子系统中的重态，并将其应用于量子系统中的热化和引力理论中的黑洞的研究。这两个看起来非常不同的问题通过引力全息学以一种非常具体的方式联系起来，它将非引力量子系统与强相互作用和高维引力理论联系起来。我们将利用我们的结果提供黑洞某些微观特性的精确描述，这将为黑洞动力学提供新的启示。我们将关注具体的量，比如在重力背景中传播的波的相移，它对应于重态。我们将研究引力有限尺寸效应，并利用这些信息，通过使用量子技术，得出与引力双星（两个相互绕轨道运行的黑洞）相关的新经典结果。该项目还将研究量子系统中的热化。想象一下，把一个很重的东西扔进一个空盒子里。这个物体是会消散成由轻粒子组成的气体（热化）并填满可用的体积，还是会继续漂浮？重物体的命运是否取决于物质成分之间相互作用的强度？在全息描述中，这个问题可以被重新表述——一个重物体的行为像黑洞吗？我们将结合量子一致性条件、全息和涉及费曼图的更传统的方法来研究这些问题。目标是了解是否所有具有大量粒子种类的量子系统都会发生热化。如果这是真的，这将意味着不同的量子系统彼此之间的相似度比之前认为的要高得多。我们还将寻找新的对称性，这些对称性强调量子场论中某些可观察到的行为。

Quantum Field Theory (QFT) is the common language of theoretical physics to describe quantum systems with a vast range of applications from mathematical physics to phenomenology. When the interaction among the quanta of the theory is weak it is possible to use standard techniques to obtain quantitative predictions. However, many important physical phenomena (such as e.g. superconductivity at relatively high temperatures, behavior of strongly coupled plasma, etc.) depend critically on strong interactions and so the traditional approach fails. In this project we will develop the mathematical machinery necessary to describe heavy states in quantum systems with strong interactions and apply it to the study of thermalization in quantum system and black holes in gravitational theories. These two seemingly very different problems are related in a very concrete way by gravitational holography, which relates non-gravitational quantum systems with strong interactions and higher dimensional theories of gravity.We will use our results to provide a precise description of certain microscopic properties of black holes, which will shed new light on the black holes dynamics. We will focus on specific quantities, such as the phase shift of a wave propagating in the gravitational backgrounds which correspond to heavy states. We will study gravitational finite size effects and use this information to derive, by using quantum techniques, new classical results relevant to gravitational binaries (two black holes orbiting each other).This project will also study thermalization in quantum systems. Imagine throwing a very heavy object into an empty box. Is this object going to dissipate into a gas of light particles (thermalize) and fill the available volume or will it just keep floating around? Does the fate of the heavy object depend on the strength of interactions between the matter constituents? In the holographic description the question can be reformulated - does a heavy object behave like a black hole? We will investigate these questions with a combination of quantum consistency conditions, holography and more traditional methods involving Feynman diagrams. The goal is to understand whether all quantum systems with a large number of species of particles thermalize. If true, this would imply that different quantum systems resemble each other much more closely than previously thought. We will also search for new symmetries which underline the behavior of certain observables in quantum field theories.